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August 30, 2012
Urs Schreiber in The Reasoner
Posted by David Corfield
In December 2008, I interviewed Tom Leinster for Kent’s in-house journal – The Reasoner. The latest version, September 2012, sees me do the same to Urs.
I’m posting this here so that any regulars, or anyone who comes here via The Reasoner, can discuss whatever strikes them in what Urs says.
The abrupt transition in The Reasoner from interview to succeeding article had people last time imagining Tom had decided to talk about ‘The Paradox of Omniscience’. Likewise, you need to guard against thinking Urs goes on to talk of ‘Personal taste ascriptions and the Sententiality assumption’.
Directed Homotopy at Liverpool
Posted by David Corfield
Zoran posted an announcement at the nForum for a EPSRC DTG studentship award for research leading to a PhD on the subject of Directed homotopy theory and -categories at Liverpool University. There’s no mention of a deadline, but it begins very soon.
The work is to be supervised by Jon Woolf, who came to my attention during our discussion on fundamental -categories with duals of statified spaces, back here. Subsequently, he wrote two papers Transversal homotopy theory and Whitney categories and the Tangle Hypothesis (with Conor Smyth) making rigorous the original Baez-Dolan idea.
Now hasn’t there got to be a connection to what Ayala and Rozenbluym are doing with sheaves over manifolds with stratified subcomplexes to reach -categories with adjoints? Will it be a case again that proves simpler than plain ?
And what about Todd Trimble’s work on surface diagrams:
This study would involve a fascinating marriage between topics in pure higher category theory (n-categories with duals) and topics in pure differential topology (stratified Morse theory).
Stratification is in the air.
August 29, 2012
Jech (1973), page 118
Posted by Tom Leinster
My friend in symplectic geometry tells me that in his field more than most, significant mistakes find their way into the published literature. But it seems that other subjects have had trouble with this too:
August 24, 2012
Brown Representability
Posted by Mike Shulman
Time for more debunking of pervasive mathematical myths. Quick, state the Brown representability theorem!
August 20, 2012
Quantum Gauge Field Theory in Cohesive Homotopy Type Theory
Posted by Urs Schreiber
Readers of this blog know that Mike Shulman and myself have had extensive discussion, over many months, about cohesive homotopy type theory. Mike has connected this to his other work on homotopy type theory as explained in his post Internalizing the External, or The Joys of Codiscreteness, and I have been trying to see how much of quantum gauge field theory can be formalized in this axiomatics, discussed for instance in the post Prequantization in cohohesive homotopy type theory.
Now, the call for submissions to
QPL 2012
Quantum Physics and Logic
10-12 October 2012, Brussels, Belgium
(website)
made us think that this may be a good occasion to finally write up something together, even if it is just an “extended abstract”. This we have done now:
Urs Schreiber and Michael Shulman, Quantum gauge field theory in Cohesive homotopy type theory (pdf, 12 pages)
Abstract. We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in gauge quantum field theory. This is a brief survey of work by the authors developed in detail elsewhere (Sh, Sc).
Maybe you’d enjoy having a look and dropping us a comment. It’s a brief survey (given the size constraints demanded for submissions of this form) of a collection of central constructions and their relations, which hopefully serves to indicate how the two seemingly disparate subjects of the title are in fact closely related.
August 13, 2012
Strings and Automorphic Forms in Topology
Posted by Urs Schreiber
This week takes place the conference
Strings and Automorphic Forms in Topology
(webpage)
intended as the pure-math satellite conference of the recent String-Math 2012 meeting :
The conference focuses on the topological aspects of the series of String-Math meetings. It aims to engage the growing number of mathematicians working on the new interactions of topology with string geometry in mathematical physics and algebraic geometry. Its main topics include topological automorphic forms, conformal field theories, the string group and topological algebraic geometry.
I have missed the first day, having only just returned from a fairly long and very off-line vacation.
Myself. I am speaking about this:
- Urs Schreiber, Higher prequantum string geometry (pdf)
I’ll be reporting from events at the conference in the comment section below.
August 8, 2012
Categorical Unification
Posted by David Corfield
A couple of postdoc positions have been advertised to work with Bob Coecke and Samson Abramsky on a research project – Categorical unification: where foundational physics, natural language and rational processes meet – in the Department of Computer Science in Oxford. In view of the Executive Summary, I’d be interested to see the full description of the project.